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SageMath
E = EllipticCurve("io1")
E.isogeny_class()
Elliptic curves in class 227850io
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
227850.k1 | 227850io1 | \([1, 1, 0, -212650, 38684500]\) | \(-1389015072282481/44431441920\) | \(-34017822720000000\) | \([]\) | \(2193408\) | \(1.9480\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 227850io1 has rank \(1\).
Complex multiplication
The elliptic curves in class 227850io do not have complex multiplication.Modular form 227850.2.a.io
sage: E.q_eigenform(10)